PACF | Cuts off after lag \(p\) | Tails off | Tails off

In this exercise, you will generate data from the AR(1) model, $$X_t = .9 X_{t-1} + W_t,$$ look at the simulated data and the sample ACF and PACF pair to determine the order. Then, you will fit the model and compare the estimated parameters to the true parameters.

Throughout this course, you will be using sarima() from the astsa package to easily fit models to data. The command produces a residual diagnostic graphic that can be ignored until diagnostics is discussed later in the chapter.

Instructions

Use the prewritten arima.sim() command to generate 100 observations from an AR(1) model with AR parameter .9. Save this to x.

Plot the generated data using plot().

Plot the sample ACF and PACF pairs using the acf2() command from the astsa package.

Use sarima() from astsa to fit an AR(1) to the previously generated data. Examine the t-table and compare the estimates to the true values. For example, if the time series is in x, to fit an AR(1) to the data, use sarima(x, p = 1, d = 0, q = 0) or simply sarima(x, 1, 0, 0).